310 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



The energy of the suction which produces these effects may be 

 inferred from the following considerations. The pressure in the 

 slender liquid mass which encircles the film is of course variable, 

 being greater in the lower portions than in the upper, but it is 

 everywhere less than the pressure of the atmosphere. Let us take 

 a point where the pressure is less than that of the atmosphere by an 

 amount represented by a column of the liquid one centimeter in height. 

 (It is probable that much greater differences of pressure occur.) At a 

 point near by in the interior of the film the pressure is that of the 

 atmosphere. Now if the difference of pressure of these two points 

 were distributed uniformly through the space of one centimeter, the 

 intensity of its action would be exactly equal to that of gravity. 

 But since the change of pressure must take place very suddenly 

 (in a small fraction of a millimeter), its effect in producing a current 

 in a limited space must be enormously great compared with that of 

 gravity. 



Since the process just described is connected with the descent of 

 the liquid in the mass encircling the film, we may regard it as 

 another example of the downward tendency of the interior of the 

 film. There is a third way in which this descent may take place, 

 when the principal component of the interior is volatile, viz., 

 through the air. Thus, in the case of a film of soap-water, if we 

 suppose the atmosphere to be of such humidity that the potential for 

 water at a level mid- way between the top and bottom of the film has 

 the same value in the atmosphere as in the film, it may easily be 

 shown that evaporation will take place in the upper portions and 

 condensation in the lower. These processes, if the atmosphere were 

 otherwise undisturbed, would occasion currents of diffusion and other 

 currents, the general effect of which would be to carry the moisture 

 downward. Such a precise adjustment would be hardly attainable, 

 and the processes described would not be so rapid as to have a 

 practical importance. 



But when the potential for water in the atmosphere differs con- 

 siderably from that in the film, as in the case of a film of soap -water 

 in a dry atmosphere, or a film of soap- water with glycerine in a moist 

 atmosphere, the effect of evaporation or condensation is not to be 

 neglected. In the first case, the diminution of the thickness of the 

 film will be accelerated, in the second, retarded. In the case of the 

 film containing glycerine, it should be observed that the water con- 

 densed cannot in all respects replace the fluid carried down by the 

 internal current but that the two processes together will tend to 

 wash out the glycerine from the film. 



But when a component which greatly diminishes the tension of the 

 film, although forming but a small fraction of its mass (therefore 



